An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation

Pundikala Veeresha, Doddabhadrappla Gowda Prakasha and Dumitru Baleanu
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Pundikala Veeresha: Department of Mathematics, Faculty of Science & Technology, Karnatak University, Dharwad 580003, India
Doddabhadrappla Gowda Prakasha: Department of Mathematics, Faculty of Science & Technology, Karnatak University, Dharwad 580003, India
Dumitru Baleanu: Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No, Etimesgut 406790, Turkey

Mathematics, 2019, vol. 7, issue 3, 1-18

Abstract: The q -homotopy analysis transform method ( q -HATM) is employed to find the solution for the fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology.

Keywords: q -homotopy analysis transform method; fractional Kolmogorov–Petrovskii–Piskunov equation; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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